Benford’s Law, Zipf’s Law and the Pareto Distribution

Over the past few weeks we’ve seen several examples of power-law distributions in real life. We saw how Benford’s Law was used to try and detect fraud in the Iranian election. And we saw how Zipf’s Law predicts the distribution of city size. I don’t think we’ve looked at the related Pareto distribution recently (it’s the basis behind the common 80/20 rule), but all three distributions often crop up for statistics that: (i) take values as positive numbers; (ii) range over many different orders of magnitude; (iiii) arise from a complicated combination of largely independent factors; and (iv) have not…

Over the past few weeks we've seen several examples of power-law distributions in real life. We saw how Benford's Law was used to try and detect fraud in the Iranian election. And we saw how Zipf's Law predicts the distribution of city size. I don't think we've looked at the related Pareto distribution recently (it's the basis behind the common 80/20 rule), but all three distributions often crop up for statistics that:

(i) take values as positive numbers;(ii) range over many different orders of magnitude;(iiii) arise from a complicated combination of largely independent factors; and(iv) have not been artificially rounded, truncated, or otherwise constrained in size.

I took those criteria from a great post from Terence Tao that delves into the ins and outs of these surprisingly common distributions, and gives some great examples.